Various data processing systems have been developed including storage systems, cellular telephone systems, and radio transmission systems. In such systems, data is transferred from a sender to a receiver via a medium. For example, in a storage system, data is sent from a sender (e.g., a write function) to a receiver (e.g., a read function) via a storage medium. A data processing function uses a data decoder circuit configured to recover originally written data, such as a data decoder included with a read channel circuit that employs information divergence based data processing circuitry. A layered decoder can be used to provide more effective trapping set handling, but may also have slower convergence. For example, in a layered decoder, a parity-check matrix can be divided into an integer number of layers, N, and an integer number of circulants, M, where message updates follow a predetermined order. The decoder first updates messages in the first layer, then messages in the second layer, and then messages in each subsequent layer through the Nth layer. Within each layer, the decoder updates the messages within each circulant one at a time, and processes the circulants sequentially in a predetermined order, such as from left to right.